Some stable difference approximations to a fourthorder parabolic partial differential equation
Authors:
G. Fairweather and A. R. Gourlay
Journal:
Math. Comp. 21 (1967), 111
MSC:
Primary 65.68
Corrigendum:
Math. Comp. 22 (1968), 246247.
MathSciNet review:
0221785
Fulltext PDF Free Access
References 
Similar Articles 
Additional Information
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G. Fairweather & A. R. Mitchell, "Some computational results of an improved ADI method for the Dirichlet problem," Comput. J. (To appear.)
 [1]
 G. Birkhoff, R. S. Varga & D. M. Young, "Alternating direction implicit methods," Advances in Computers, Vol. 3, Academic Press, New York, 1962. MR 0168131 (29:5395)
 [2]
 J. Crank & P. Nicolson, "A practical method for numerical evaluation of solutions of partial differential equations of the heatconduction type," Proc. Cambridge Philos. Soc., v. 43, 1947, pp. 5067. MR 8, 409. MR 0019410 (8:409b)
 [3]
 J. Douglas, Jr., "The solution of the diffusion equation by a high order correct difference equation," J. Math. Phys., v. 35, 1956, pp. 145151. MR 19, 884. MR 0090875 (19:884f)
 [4]
 E. C. Du Fort & S. P. Frankel, "Stability conditions in the numerical treatment of parabolic differential equations," MTAC, v. 7, 1953, pp. 135152. MR 15, 474.
 [5]
 D. J. Evans, "A stable explicit method for the finitedifference solution of a fourthorder parabolic partial differential equation," Comput. J., v. 8, 1965, pp. 280287. MR 0189264 (32:6691)
 [6]
 H. O. Kreiss, "Über implizite Differenzmethoden für partielle Differentialgleichungen," Numer. Math., v. 5, 1963, pp. 2447. MR 27 #5376. MR 0155442 (27:5376)
 [7]
 M. Lees, "Alternating direction and semiexplicit difference methods for parabolic partial differential equations," Numer. Math., v. 3, 1961, pp. 398412. MR 25 #5605. MR 0142212 (25:5605)
 [8]
 A. R. Mitchell & G. Fairweather, "Improved forms of the alternating direction methods of Douglas, Peaceman and Rachford for solving parabolic and elliptic equations," Numer. Math., v. 6, 1964, pp. 285292. MR 30 #4391. MR 0174184 (30:4391)
 [9]
 B. Numerov, Publ. Observ. Astrophys. Central Russia, v. 2, 1933, p. 188.
 [10]
 D. W. Peaceman & H. H. Rachford, "The numerical solution of parabolic and elliptic differential equations", J. Soc. Indust. Appl. Math., v. 3, 1955, pp. 2841. MR 17, 196. MR 0071874 (17:196d)
 [11]
 R. D. Richtmyer, "Difference methods for initial value problems," Interscience Tracts in Pure and Applied Mathematics, Tract 4, Interscience, New York, 1957. MR 20 #438. MR 0093918 (20:438)
 [12]
 J. Douglas, Jr., "The application of stability analysis in the numerical solution of quasilinear parabolic differential equations," Trans. Amer. Math. Soc., v. 89, 1958, pp. 484 518. MR 24 #A1521. MR 0131673 (24:A1521)
 [13]
 M. Lees, "A priori estimates for the solutions of difference approximations to parabolic partial differential equations," Duke Math. J., v. 27, 1960, pp. 297312. MR 22 #12725. MR 0121998 (22:12725)
 [14]
 R. S. Varga, Matrix Iterative Analysis, PrenticeHall, Englewood Cliffs, N. J., 1962. MR 28 #1725. MR 0158502 (28:1725)
 [15]
 G. Fairweather & A. R. Mitchell, "Some computational results of an improved ADI method for the Dirichlet problem," Comput. J. (To appear.)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718196702217852
PII:
S 00255718(1967)02217852
Article copyright:
© Copyright 1967
American Mathematical Society
